Can Blender run headless on an ARM processor?
I have run Blender on an ARMv7 CPU somewhat similar to the one the Raspberry Pi 2 model B uses, so I think Blender has no problems running on this architecture.

In practice, the problem would be processing power. On my Google Nexus 4, which has a quad-core 1.5 GHz Qualcomm Krait CPU, it took well over an hour to render Mike Pan's BMW scene:



This table on Wikipedia seems to show that the Krait in my phone would perform about the same as, or perhaps a bit better than, the Cortex A7 in the Raspberry Pi 2. Additionally, the Pi runs at 0.9 rather than 1.5 GHz. Would a setup with CPUs like these be able to render images? Almost certainly. Would you want to wait for them to do it? Personally, I think you wouldn't.